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INDEX, Sl. No, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10, , Topic, Theorems on Triangle, Theorems on Circle, Construction, Ogive curve, Elimination and graphical method, Mean, median and mode, Quadratic equation (Formula and nature of roots), Co-ordinate geometry, Arithmetic Progression, Formula, , Page Number, 4&5, 5, 6to8, 9to10, 10to12, 12to13, 14, 15, 15 to 16, 16, , Possibility of marks, 4-5+1(Statement), 3, 9, 3, 7, 3, 4, 7, 6, 3, , Total 50, 11, 12, , (Weakly Two exam) Target 45 question Paper-1,2,3,4, Target 45 Question Paper-5,6,7,8,9, , 17 to19, 18 to21, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 3 | Page

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THEOREM(7 to 8 marks), Theorem 1 : Thales Theorem OR Basic Proportionality Theorem, , “A line drawn parallel to one side of a triangle divides the, other two sides in the same ratio”., Data : In Δ ABC, DE, , Theorem 3(Areas of Similar Triangles), “The areas of two similar triangles are proportional to the, squares of their corresponding sides”., Data: Δ𝑌𝐸𝐷 ~ Δ.𝐷𝐵𝐷, 𝑌𝐸, 𝐷𝐵, , BC., , 𝑌𝐷, 𝐷𝐷, , 𝐸𝐷, 𝐵𝐷, , To Prove:, , To Prove :, , Construction: Draw AL ⊥ BC and DM ⊥ EF., , Construction : Draw DM ⊥ AC and EN ⊥ AB., Proof :, , ------- (1), , =, , =, , ---------- (2), , ΔBDE and ΔDEC stand on the same base DE and between the, same parallel lines DE and BC∴.Area of Δ 𝐸𝐷𝐵 = Area of Δ𝐷𝐵𝐷, So from equations (1) and (2), we have, , =, , . Hence proved., , Theorem 2 (A A Criterion):, “If the corresponding angles of two triangles are equal, then, their corresponding sides are in the same ratio”, Data : In Δ ABC and Δ DEF,∠A = ∠D, ∠B = ∠ E and ∠C =∠ F, , =, , Proof :, , ----> (1), , In Δ ABL and Δ DEM,∠B =∠ E By data∠L =∠ M, ∴Δ𝑌𝐸𝐴 ~ Δ 𝐷𝐵𝐷, [AA Criterion], , [ Right angles], , - --- - > (2), , But, Substitute (2) in (1), , Hence proved., , Theorem 4(Pythagoras Theorem):, “In a right angled triangle, the square on the hypotenuse is, equal to the sum of the squares on the other two sides”, Data : ABC is a right angled triangle , ∠B = 900, To Prove : AC2 = AB2 +BC2, Construction : Draw BD ⊥ AC., , To Prove :, , Proof :, , In Δ ABC and Δ ADB,, ∠A =∠ A [Common angles], ∠B =∠ D [Right angles], ∴Δ𝑌𝐸𝐷 ~ Δ 𝑌𝐷𝐸, [AA Criterion], , Construction: Mark the points, , X and Y on AB and AC such that, AX =DE and AY =DF., , Proof : In Δ AXY and Δ DEF,, ∠A = ∠D [By data], AX = DE [By Construction], AY = DF [By construction] ⇒∴Δ 𝑌𝑋𝐴≅ Δ𝐷𝐵𝐷 [SAS congruence], ∴ ∠ 𝑋= ∠𝐵 [CPCT]⇒ ∠B =∠ E. ∴∠X=∠B ⇒XYǁ BC, Corollary of B.P.T], , [By Substitution]. Hence proved., , AB2 = AC AD-----(1), Similarly, In Δ ABC and Δ BDC, ∠C =∠ C, [Common angles], ∠B =∠ D [Right angles], ∴Δ𝑌𝐸𝐷 ~ Δ 𝐸𝐷𝐷 [AA Criterion] ⇒, BC2 = AC DC------- (2)Adding equations (1)and (2),, AB2 +BC2 = AC, AB2, , +BC2, , =, , AC2, , AD+AC, , DC.= AC(AD+ DC)= AC, , AC, , Hence proved., , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 4 | Page

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Theorem 5 (Converse of Pythagoras Theorem):, In a triangle, if square of one side is equal to the sum of the, squares of the other two sides, then the angle opposite the, first side is a right angle., Data : In a triangle ABC in which, AC2= AB2 + BC2, To Prove : ∠B=900., Construction: To start with, we construct a, , Circle theorem 2, “The two tangents drawn from an external point to a circle, are equal”., Data : O is the centre of the, circle .P is an external point ., AP and BP are tangents to the, circle., , Δ PQR right angled at Q such that PQ=AB To Prove : AP =BP, and QR = BC., Proof : In Δ AOP and Δ BOP,, Proof : Now, from ΔPQR, we have : PR2 = PQ2 + QR2 (Pythagoras, ∠OAP =∠OBP, [Right angles], Theorem, as ∠ Q = 90°) or,, OA =OB, [Radii of the same circle], PR2 = AB2 + BC2 (By construction)------- (1), 2, 2, 2, OP=OP, [Common side], But AC = AB + BC (Given)-------------- (2), ∴ΔAOP ≅ΔBOP [RHS Theorem], So, AC = PR ------------(3), [From (1) and (2)], ∴ AP=BP [C.P.C.T], Now, in Δ ABC and Δ PQR,, Hence proved., AB = PQ (By construction), BC = QR (By construction), AC = PR [Proved in (3) above], So, Δ ABC ≅ Δ PQR (SSS congruence), Therefore, ∠ B = ∠ Q (CPCT), But ∠ Q = 90° (By construction) ⇒So, ∠ B = 90°, , Circle theorem 1, “The tangent at any point of a circle is perpendicular to the, radius drawn at the point of contact”., Data: O is the centre of the circle .XY is the, tangent to the circle at the point P .OP is the, radius drawn at the point of contact P., , To Prove : OP ⊥ XY., Construction : Take a point Q on XY .Join OQ., Proof : OQ=OR+RQ ⇒OQ=OP+RQ (OP=OR), ⇒ OQ>OP ⇒∴OQ is longer than OP., So, OP is the smallest distance of the point O from the line XY., , ∴ OP ⊥ XY., Hence proved., SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 5 | Page

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CONSTRUCTIONS (TARGET 9marks), , TO DIVIDE THE LINE SEGMENT IN THE GIVEN RATIO, , 1) Draw a line segment of length 7 cm and divide it in the ratio of 2:1, STEPS:, 1. Draw a line AB with the, measure 7 cm, 2. Draw a line AX such that it, makes an acute angle., 3. Make 2+1= 3 equal parts on, AX., 4. Join last part A3 to B., 5. Draw a parallel line A2C to A3B, , I CAN DO IT, 1) Draw a pair of tangents to a circle of radius 5 cm, such that the, radii are inclined at an angle 600, 2) Draw a pair of tangents to a circle of radius 5 cm, such that the, radius is inclined at an angle 1250, 3) Draw a pair of tangents to a circle of radius 3.5 cm, such that the, radii are inclined at an angle 800, 4) Draw a pair of tangents to a circle of radius 4 cm, such that the, radii are inclined at an angle 750 . and write the measure of its, length., 5) Draw a pair of tangents to a circle of radius 3 cm, such that the, radii are inclined at an angle 700., , Type 2 : Angle between the tangents is given., , AC: CB = 2:1, , I CAN DO IT, , 2) Draw a line segment AB of length 8 cm and divide it in the ratio of 3:2., 3) Draw a line segment of length 7.6 cm and divide it in the ratio of 4:2., Measure the two parts., 4) Draw a line segment of length 12 cm and divide it in the ratio of 5:2, 5) Draw a line segment of length 9 cm and divide it in the ratio of 3:4, , 1) Draw a pair of tangents to a circle of radius 5 cm, which are, inclined at an angle of 600. Measure the length of the tangents., Angle between the radii= 1800-600= 1200, STEPS:, 1) Draw a circle of radius 5, cm, 2) Make 1200 between, radii OA and OB., 3) Draw perpendicular line, at A and B and produce, to intersect at P., 4) PA and PB are the, tangents, , CONSTRUCTION OF TANGENTS TO A CIRCLE, Type 1 : Angle between the radii is given., , 1) Draw a pair of tangents to a circle of radius 3 cm, such that, the radii are inclined at an angle 1400., , STEPS :, 1), Draw a circle of radius 3, cm., 2) Make an angle of 1400, between the radii OP and OQ., 3) Draw perpendicular line at P, and Q and produce to intersect at, R., 4) RP and RQ are the tangents., , RP and RQ are the tangents., , PA and PB are the tangents, , I CAN DO IT, , 2) Draw a pair of tangents to a circle of radius 3.5cm, such that the, angle between the tangents is 900, 3) Draw a pair of tangents to a circle of radius 4cm, which are inclined, at an angle of 1200, 4) Draw a pair of tangents to a circle of radius 3cm, which are inclined, at an angle of 600, 5) Draw a pair of tangents to a circle of radius 3cm, which are inclined, at an angle of 700, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 6 | Page

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6) Draw a pair of tangents to a circle of radius 3.5 cm, which are, inclined at an angle of 800, 7) Draw a pair of tangents to a circle of diameter 6 cm, which are, inclined at an angle of 550, 8) Draw a pair of tangents to a circle of radius 3.5 cm, which are, inclined at an angle of 800, 9) Draw a pair of tangents to a circle of radius 4 cm, which are inclined, at an angle of 1000, 10) Draw a pair of tangents to a circle of radius 5 cm, which are, inclined at an angle of 600 . Measure the length of the tangents., , Type 2 : Construction of tangents from an external point., 1. Draw a circle of radius 3.5 cm from a point 8 cm away from the center;, construct the pair of tangents to the circle. Measure the tangents and, write., , Type 3 : Construction of tangents on the circumference of the, circle, 1) Draw a circle of radius 2.5 cm and Construct a chord of length 3, cm. and Draw the tangents at the end points of the chord., STEPS:, 1) Draw a circle of radius 2.5 cm, 2) Draw a chord AB of length 3 cm, 3) Draw perpendicular line at A, and B. Produce them to meet, at P., 4) PA and PB are the tangents., , Tangents PA= PB= 7.2 cm, STEPS:, 1) Draw a circle of radius 3.5 cm., 2) Draw a line segment OP of length 8 cm., 3) Draw perpendicular bisector of OP, 4) With the midpoint of OP as centre draw a circle points O and P on it., 5) Join the intersection points A and B to P., 6) PA and PB are the tangents., , I CAN DO IT, 1. Draw a circle of radius 5cm. from a point 5cm away from the circle,, construct the pair of tangents to the circle., 2., Draw a circle of radius 4cm. from a point 8cm away from the center,, PA and PB are the tangents., construct the pair of tangents to the circle., I CAN DO IT, 3., Draw a circle of diameter 6 cm. from a point 8cm away from the center,, 2) Draw a circle of radius 5 cm and Construct a chord of length 7 cm. and, construct the pair of tangents to the circle., Draw the tangents at the end points of the chord., 4., Draw a circle of radius 3 cm. Take two points P and Q on one of its, 3) Construct a tangent to a circle of radius 4 cm at any point P on its, extended, diameters each at a distance of 7 cm from its centre. Draw, circumference., tangents, to, the, circle from these two points P and Q., 4) Draw a circle of radius 3 cm and draw a diameter AB. Construct the, 5. 6)Draw two concentric circles of radii 3, and 5 . Taking a point on the, tangents at A and B., outer, circle,, construct, the, pair, of, tangents, to, the inner circle., 5) Draw a circle of radius 3 cm and Construct a chord AB of length 5 cm., 6. Draw two concentric circles of radii 3, and 5, . Construct a, and Draw the tangent at point B., tangent, to, smaller, circle, from, a, point, on, the, larger, circle., Also, measure its, 6) Draw a circle of radius 4.5 cm and Construct a chord PQ of length 7 cm., length., and Draw the tangent at the point P., SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 7 | Page

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Construction of Similar Triangles, Type 1: When proper fraction (ratio) given :, 1) Construct a triangle of sides 4 cm , 6 cm and 4.5 cm and then a triangle, similar to it whose sides are of the corresponding sides of the first triangle., , Type 2: When improper fraction (ratio) given :, 1)Draw a triangle ABC with sides AB = 5cm, BC = 4 cm and ∟ABC 60, 0 Then, , construct a triangle whose sides are of the corresponding, sides of triangle ABC., , ABC ∼ AB’C’, STEPS:, 1), 2), 3), 4), 5), 6), , Draw a triangle ABC with sides 4 cm, 6 cm and 4.5 cm., Draw AX such that which makes an acute angle., Make equal 3 parts on AX., Join 3rd point ie A3 to B., Make same measure of angle A3 at 2nd point ie at A2 Join A2B’, Make same measure of angle B at point B’ . Produce C’, , I CAN DO IT, 1), Construct a triangle of sides 4 cm , 5 cm and 6 cm and then a triangle, similar to it whose sides are of the corresponding sides of the first triangle., 2), Construct a triangle of sides 4 cm , 5 cm and 6 cm and then a triangle, similar to it whose sides are of the corresponding sides of the first triangle., 3), Construct a triangle of sides 5 cm , 6 cm and 7 cm and then a triangle, similar to it whose sides are of the corresponding sides of the first triangle., 4), Draw a triangle ABC with sides AB 5 cm, BC 6 cm and ∟ABC 600., Then construct a triangle whose sides are 2:3 of the corresponding sides of, triangle ABC., , ABC ∼ AB’C’, STEPS:, 1), 2), 3), 4), 5), 6), , Draw a triangle ABC with AB= 5 cm, BC= 4 cm and ∟ABC 600, Draw AX such that which makes an acute angle., Make equal 7 parts on AX., Join 5th point ie A5 to B., Make same measure of angle as A5 in 7th point ie at A7 . Join A7B’, Make same measure of angle B at point B’ and Produce to C’, I CAN DO IT, , 5) Construct a triangle of sides 5 cm , 6 cm and 7 cm and then a triangle, similar to it whose sides are of the corresponding sides of the first, triangle., 6) Draw a triangle ABC with sides AB 6cm, BC 5cm and ∟ABC 800 ., Then construct a triangle whose sides are of the corresponding sides of, triangle ABC., , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 8 | Page

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7) Construct a triangle ABC with sides AB 6cm and ∟BAC 500 and, ∟ABC 600. Then construct a triangle whose sides are 1 of the, corresponding sides triangle ABC., 8) Construct a triangle ABC with sides BC= 4.5cm and AB= 5.5 cm and, ∟A 550 . Then construct a triangle whose sides are the corresponding, sides of triangle ABC., 9) Draw a right triangle in which the sides (other than hypotenuse ) are, of lengths 8 cm and 6 cm, then construct another triangle whose sides are, of times the corresponding sides of the given triangle., 10) Draw a triangle ABC with side base BC= 8 cm and altitude 4 cm, and, then construct another triangle whose sides are times the corresponding, sides of the isosceles triangle ABC., 11) Draw a right triangle in which the sides (other than hypotenuse ) are, of lengths 4 cm and 3 cm, then construct another triangle whose sides are, of times the corresponding sides of the given triangle., 12) Construct a triangle of sides 4 cm , 5 cm and 6 cm and then a triangle, similar to it whose sides are of the corresponding sides of the first, triangle., , Ogive Curve: (Target-3marks), 1. Draw more than ogive curve for following data., CI, 0-50, 50-100 100-150 150-200 200-250 250-300, f, 12, 18, 27, 20, 17, 6, It should be converted like this., CI, F, CI, f, (x,y), 0-50, 12, More than 0, 100 (0,100), 50-100, 18, More than 50, 88 (50,88), 100-150, 27, More than 100 70 (100,70), 150-200, 20, More than 150 43 (150,43), 200-250, 17, More than 200 23 (200,23), 250-300, 6, More than 250 6, (250,6), , Dear students this question can also be asked like this., CI, , More than More than, 0, 50, CF 100, 88, , More than, 100, 70, , More than, 150, 43, , More than More, More than, 200, than 250 300, 23, 6, 0, , If they given question like this then you can plot graph directly., , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 9 | Page

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2.Same question for less than type draw more than ogive curve for, following data., CI, F, , 0-50, 12, , 50-100, 18, , 100-150, 27, , 150-200, 20, , 200-250, 17, , Pair of Linear Equation in, two variables, , 250-300, Step:1 To get 1mark study this table:(a1x+b1y=c1:a2x+b2y=c2), 6, Sl.No, , It should be converted like this., CI, F, CI, 0-50, 12, less than 50, 50-100, 18, less than 100, 100-150, 27, less than 150, 150-200, 20, less than 200, 200-250, 17, less than 250, 250-300, 6, less than 300, , 1., , f, 12, 30, 57, 77, 94, 100, , (x,y), (50,12), (100,30), (150,57), (200,77), (250,94), (300,100), , Compare the Graphical, ratio, Representation, Lines intersecting, , Algebraic, Interpretation, Only one solution, i.e(unique solution), , Consistency, Consistent, , 2., , Lines are coincident, , Many solution, i.e(infinite solution), , Dependent and, consistent., , 3., , Lines are parallel, , No solution (Zero, solution), , Inconsistent, , Step:2 To get 2mark, (Solve these linear equation by elimination method):, Type 1.Solve x+3y=6 and 2x-3y=6., Solution: x+3y=6-------(1) 2x -3y=6-------(2), Adding these we get, x +3y=6, 2x - 3y=6, 3x+(0)y=12, 3x=12 ⇒ x= ;x=4 => consider (1) x+3y=6 =>4+3y=6,  3y=6-4=2 ⇒y= ;, , So x=4 and y=, , are the solution., , Type 2. Solve 2x+y-6=0 and 6x+2y-4=0., Solution: 2x+ y-6=0 => 2x+ y=6-------(1), 6x+2y-4=0 => 6x+2y=4-------(2) Here we eliminate y-coordinate. To, eliminate y we need to multiply (1) by 2 and subtract., 4x+ 2y= 12-------(1), Dear students this question can also be asked like this., 6x+ 2y= 4-------(2), CI Less than 0 less than less than 100, less than less than less than less than, (-) (-) =(-), 50, 150, 200, 250, 300, -2x=8 => x= = - 4 x= - 4 ; substitute in (1) 2x+y=6, CF 0, 12, 30, 57, 77, 94, 100, => 2(-4)+y=6 =>-8+y=6 => y=6+8 =>y=14 So x=-4; y=14 are the solution., SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 10 | Page

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Type 3: Solve 3x+4y=2 and 2x-3y=7., Solution: 3x+4y=2 - - - - - - - -(1), 2x-3y=7 - - - - - - - -(2), Here both x and y have different coefficients in equations (1) and, (2). So make the coefficient of any of the variable (either x or y) to be same, in both equations. Multiply equation (1) by 2(co efficient of x in (2)) and, equation (2) by 3(co efficient of x in (1)).,  6x+8y=4, 6x-9y=21, On subtraction, 17y = -17,  y = -1, Now substitute y= -1 in equation (1), we get, 3x+4(-1) =2  3x -4 = 2  3x = 2 + 4, 3x = 6  x = 2 The solutions are x= 2 and y = -1., , Solve the following for X and Y:, I CAN DO IT, , Step3: Graphical solution of pair of linear equation by, getting perfect you will get 4marks in your exam:, 1.Solve the following pair of linear equations in two variables by graphical, method :x + y = 7 and 3x – y = 1, Solution:x+y=7, 3x-y=1, x, 0, 1, 2, 3, x, 0, 1, 2, 3, 4, y 7, 6, 5, 4, y, -1, 2, 5, 8, 11, , Here lines intersect at(2,5) so solution is x=2 and y=5., , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 11 | Page

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2.Solve the following pair of linear equations in two variables by graphical, method :y =2x-2 and y =4x-4, Solution: y=2x-2, y=4x-4, x, 0, 1 2, 3, 4, x -1 1, 2, 3, y, -4, 0 4, 8, 12, y -4 0, 2, 4, , Mean, Median and Mode : (Target-3marks), Mean: Mean is the ratio of sum of all observations to the total number of, observations., Median : The middle most observation in an orderly arranged data distribution, is called Median., Mode: The most repeated observation in a data distribution is called Mode., , Formulae to find mean, median and mode:, 1), Mean =  fx where ‘f ’ is frequency and ‘x ’ is class mark of class, , f, , interval, , 2), , Median =, , n,   cf, l2,  f, , , , , h, , , , where, , l – Lower limit of median class n- Number of observations h – Class size, cf – Cumulative frequency of class preceding the median class, f- Frequency of median class., , Mode = l  , , f1  f 0 , h,  2 f1  f 0  f 2 , , Here lines intersect at (1,0) so solution is x=1 and y=0, For practice: Solve these questions by elimination method and also solve by, graphical method.*, 1.3x+2y=1;5x-3y=2, 5.3x+2=y; y-3=4x, 9.3x+2y=5;5x-3y=1, 13.3x+5y=4;x-5y=8, 17.x-y=4; x+y=10, , 2.5x-3y=2;4x-y=1, 6.5x+y=7;x-3y=5, 10.3x-y=7;x+3y=5, 14.y-x+2=0;x-2y-4=0, 18.2x-y-2=0; x+y=6, , 3.2x+3y=2;3x-1=4y, 7.y-x=2; 2x-y=-2, 11.4x-y=3; 3x-2y=1, 15.2x+y=3;x+3y=-10, 19.x+y=10;x-y=2, , l – Lower limit of the modal class h – Class size, f1- Frequency of modal class f0- Frequency of class preceding modal class, f2 – Frequency of class succeeding modal class., Example 1): Calculate mean, median and mode for the following data, distribution., C-I, , 0-10, , 10-20, , 20-30, , 30-40, , 40-50, , F, , 6, , 8, , 7, , 3, , 1, , Solution: To find mean, 4.5x+y=1;x-y=8, 8.3x+y=7; 4x-y=2, C-I, f X, fx, 12.2x-y=7; x-3=4y, 0-10, 6, 5, 30, 16.y=2x-2; y=4x-4, 20.2x+y=8;x+2y=7, 10-20 8 15, 120, , * Solve daily one problem from above on elimination method and graphical, method to get 6m., , where,, , 20-30, 30-40, 40-50, , 7, 3, 1, , 25, 35, 45, , 175, 105, 45, ,  Mean x   fx, , f, , =, = 19., , = 25, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , = 475, , 12 | Page

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To find median,, C-I, f Cf, , Here ‘n’ is odd so consider (, , th, , observation., ,  n  1   25  1   26 , th, , ,      13 observation exists in, 2, 2, 2, ,  ,   , 10-20 8 14, the class interval (10-20). (By observing cf column, we, can find it)., 20-30 7 21,  (10-20) is median class., 30-40 3 24, Here, Lower limit of median l= 10, Number of observations n =25, 40-50 1 25, Cf of class preceding median class cf = 6, Frequency of median class f = 8 and Class size h = 10., n=25, , 0-10, , 6, , 6, , n,  cf,  Median= l   2,  f, , , , , h, , , , =, ,  25, , =,  2  6, 10  ,   10,  8 , , , , 12.5  6 , 10  ,  10,  8 , ,  6.5 , = 10    10, =10 + 8.125  Median =18.125,  8 , To find Mode,, Here the class (10-20) has the highest frequency ‘8’ so it is, C-I, F, called modal class., 0-10, 6,  Lower limit of modal class l =10, Size, of class interval h= 10, 10-20, 8, Frequency of modal class f1 = 8, 20-30, 7, Frequency of class preceding modal class f0 = 6, Frequency of class succeeding modal class f2 = 7, 30-40, 3, , , f f, , , , 1, 0,  Mode = l  , h, 2, f, , f, , f2 , 0,  1,  86 ,  2 , 2, 10 = 10  , = 10  , 10 = 10    10 =, , , 16  13 , 3,  2(8)  6  7 , 10 +6.66, =16.66, Note: 1) If two class intervals have highest frequencies then we have to find, mode for both class intervals., 2) If the first class interval has highest frequency then f0 =0, 3) If the last class interval has highest frequency then f 2 =0, If they given question like this then you can plot graph directly., , 40-50, , 1, , I CAN DO IT, For practice: Find mean, median, mode and draw less than and more than ogive, curve for the following data. (To achieve 3m for mean,median and mode) and 3m, for ogive. *, , C-I, F, C –I, F, C-I, F, , 0-10, 4, 0-5, 5, , 20-30, , 3, 5-10, 7, , 0-5, 4, , C-I, F, , 10-20, 5, , 10-15, 6, , 25-30, 4, 15-20, , 5, , 6, , 3-5, , 7, , 20-25, 2, , 5-7, , 8, , 1, , 20-25, 3, , 10-15, , 3, , 40-50, , 2, , 15-20, 5, , 5-10, , 1-3, , 30-40, , 7-9, , 2, , 9-11, , 2, , 1, , C-I, , 15-20, , 20-25, , 25-30, , 30-35, , 35-40, , 40-45, , 45-50, , 50-55, , F, , 3, , 8, , 9, , 10, , 3, , 0, , 0, , 2, , C-I, F, , 500-520, 12, , C-I, F, , 11-13, 7, , 520-540, 14, , 13-15, 6, , 540-560, 8, , 15-17, 9, , 17-19, 13, , 560-580, 6, 19-21, 20, , 580-600, 10, , 21-23, 5, , 23-25, 4, , C-I 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100, F, , 5, C-I, F, C-I, F, , 3, , 4, , 0-5, , 5-10, 6, , 4, 0-100, 15, , Answers:, 1) Mean = 20.33, 2) Mean = 13.5, 3) Mean = 12.25, 4) Mean = 4.2, , 3, , 3, , 4, , 10-15, 3, 100-200, 10, , 7, 15-20, 2, , 200-300, 17, , Median = 21, Median = 12.5, Median = 13, Median = 3.75, , 9, , 7, , 8, , 20-25, 5, 300-400, 12, , 400-500, 6, , Mode = 24, Mode = 8.33, Mode = 16, Mode = 3.28, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 13 | Page

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CO-ORDINATE GEOMETRY:, 1) Find the distance of a point (4, -3) from the origin.(1m), Solution: We know that formula for distance from origin is, d=, =, d= 6, d= 5 d=5 units, I CAN DO IT, , 1.Find the distance of a point (2, -3) from the origin., 2.Find the distance of a point (-6, -8) from the origin., 3.Find the distance of a point (-5, 12) from the origin., 4.Find the distance of a point (7, -24) from the origin., 5.Find the length of diameter of a circle whose centre is (-4, 3) which passes, through the origin., , 2) Find the distance between the points (2, 4)and (5, 8).(2m), Solution: We know that formula for distance from origin is, d=, =, 5, 8, d=, d=, 6, d= 5 =>d=5 units, I CAN DO IT, , 1.Find the distance between the points (-3, 5)and (3, -3)., 2.Find the distance between the points (-7, 5)and (6, 3), 3.Find the distance between the points (-12, 5)and (13, 5), 4.Find the distance between the points (-1, 5)and (6, 5), 5.Find the distance between the points (-6, 5)and (8, 5), , 3) Find the perimeter of triangle whose vertices are (5, 2), (-3, 4) and, (2, -5)., (3m), Solution:, x1=5,x2=-3,x3=2, y1=2,y2=4,y3=-5, Area of triangle= [x1(y2-y3)+x2(y3-y1)+x3(y1-y2)], = [5(4-(-5))+(-3)((-5)-2)+2(2-4)], = [5(4+5)-3(-5-2)+2(2-4)], = [5x9+3x7+2x(-2)], = [45+21-4], = [62], =31 square units, , 4) Find the type of triangle whose vertices are,, i)(1, 0), (-4, -2) and (4, -2), iii)(4, 9), (4, 3) and (8, 6), v)(-5, 6), (-10, 3) and (-6, 3), , ii)(2, 6),(-2, 3) and (6, 3), iv)(4, -5), (-3, -7) and (4, -7), , 5) Find the areas of triangles whose vertices are given below., 1.(2, -1) , (3, 2) and (5, -3), 2.(-3, 1) , (-4, -3) and (2, 1), 3.(-2, 1) , (4, 5) and (-1, -4), 4.(5, 6) , (3, -7) and (-3, -5), 5.(3, 2) , (5, -1) and (4, 0), , 6) (3, 0) , (-2, -3) and (5, -2), 7) (5, -3) , (2, -5) and (-3, 4), 8) (-1, -4) , (-5, -6) and (3, 2), 9) (-6, -3), (-8, -1) and (1, 0), 10) (0, 8), (-8, 0) and (0, 0), , 6) Find the perimeters of triangles whose vertices are given below., i)(1, 0), (-4, -2) and (4, -2), iii)(4, 9), (4, 3) and (8, 6), v)(-5, 6), (-10, 3) and (-6, 3), , ii)(2, 6),(-2, 3) and (6, 3), iv)(4, -5), (-3, -7) and (4, -7), , 7) Find the value of ‘k’ if the given points are collinear., 1) (4, k) (3, -2) and (2, 1), 2) (-1, 2), (-3, 4)and (k, 1), 3) (3, 1), (5 -2) and (2, -k), 4) (k, 2), (3, -1) and (5, 2), 5) (-1, -3), (k, -3) and (1, 2), , 6) (3, k) , (-2, -3) and (5, -2, 7) (5, -3), (4, k) and (7, -2), 8) (k, -3), (6, 5) and (4, 8), 9) (-3, -5), (-4, 5) and (0, k), 10) (6, k), (k, 2) and (-2, -3), , Arithmetic progressions, Find an for the following., , 1) In an A.P.If a=5, d=3, then find 10th term., Solution: Given a=5, d=3, W.K.T. a n  a  (n  1)d, , a10  5  (10  1)(3), a10  5  (9)(3), a10  5  27  32, th,  The 10 term of the A.P. is 32., For practice:, 1. a=3, d=2, a15=?, 3. a= -2, d=5, a10=?, 2. a=4, d=3, a20=?, 4. a=-1, d= -3, a40=?, Find number of terms for the following., 1. 2, 5, 8,………98, 5. 8, 4, 0,………..-48, 2. 1, 4, 7, ………100, 6. 12, 7, 5, ……..-138, 3. 10, 4, 7,………-47, 7. 1, 5, 9, ………57, 4. -3, -8, -13,……..-98 8. 3, 5, 7, ……..99, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 15 | Page

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TRIGONOMETRY, , Find the A.P. for the following., 1. a12=35, a18=53 find a20., 2. a13=37, a17=49 find a15., 3. a5=-23, a15=-73 find a25., 4. a22= -76, a30= -108 find a50., , 5. a32=65, a40=81 find a26., 6. a8= -15, a15=-29 find a12., 7. a7=15, a16=42 find a20., 8. a5= -28, a10= -58 find a30., , 1. One mark questions, 1. If sin  = 3 find all trigonometric ratios., 5, , 2. If cot  = 12 find all trigonometric ratios., 3. If sec =, , Find Sn for the following., Ex:1) Find the sum of A.P. 1+5+9+ ……….. upto 20 terms., Solution: Given A.P. is 1+5+9+………… upto 20 terms,  a=1, d=4, n=20, Sn=?, n, W.K.T. S n  2a  n  1)d , 2, 20, 2(1)  (20  1)(4),  S 20 , 2, S 20  102  (19)(4),  S 20  10(2  76) = 10(78)=780.,  The sum of first 20 terms is 780., For practice:, 1.2+5+8+…………upto 20 terms., 6. 3+5+7+ ………..+45., 2.1+4+7+…………upto 30 terms., 7. 3+8+13+………..+63., 3.6+4+2+…………upto 25 terms., 8. 7+12+17+………+87., 4.-3-1+1+3+………upto 15 terms. 9. 4+9+14+……….+104., 5.10+6+2+……….upto 12 terms., 10.5+3+1+…..........+(-33)., 6.Find the sum of first 20 natural numbers., 7. Find the sum of first 30 natural numbers., 8. Find the sum of first 15 odd numbers., 9. Find the sum of first 25 odd numbers., 10. Find the sum of first 12 even numbers., 11. Find the sum of first 18 even numbers., COMPLEMENTARY RATIOS, 1. Evaluate the following., 0, 1. sin 23 0, cos 67, , 2., , 5.tan620-cot280, , cos ec 42 0, sec 48 0, , 0, 3. tan 36 0, cot 54, , 6. cosec150-sec750, , 7. sin260+cosec420-sec480-cos640, 3 tan 44  2 cot 46, 9. 5 cot 46  2 tan 44, , 4.sin540-cos360, 8. 2 cos ec 64  sec 26, 2 sec 26  cos ec 64, , 3 sin 50  2 cos 40 3 cos 50  4 sin 40, , 10. 5 cos 50  4 sin 40 2 cos 40  sin 50, , 5, , 7, 3, , find all trigonometric ratios., , 4. If cos  = 5 find all trigonometric ratios., 8, , 5. Express tan  in terms of all trigonometric ratios., Express cosec  in terms of all trigonometric ratios, 2. Standard Angles: Evaluate the following., Ex: 1) Evaluate 2 tan 45  3sin 30, 2 cosec 30  sec 60, , 7, 1, 3, 2, (, 1, ), , 3, (, ), 2, , 2 tan 45  3 sin 30, 2 =, 2 = 2 =7, Solution:, =, 2 cos ec30  sec 60, 2 4, 42, 2(2)  2, , 3. For practice:, 0, 0, 45 0, 1. sin 60  cos0 30  2 cot, 0, , sin 45  sec 60, cos, 45 0  2 sec 30 0, 3., 2 cos ec 45 0  3 cot 30 0, , 5. 2 tan2450+cos2300-sin2600, 7. sin 30  cos0 ec30, 0, , 0, , cot 45, , 9., , sec 30 0  2 cos 60 0  cot 45 0, 3 tan 45 0  2 cos ec 60 0, , 0, ec30 0, 11. 3 sec 30  2 cos, 0, , 3 cos 45, , 4 tan 45 0  3 cot 30 0, 13., 3 cos ec 45 0  sec 45 0, 2, 0,  3 cos 2 30 0, 15. 4 sec 45, 0, 2, 0, , 0, 45 0  cos ec30 0, 2. tan 30  cot, 0, 0, , sec 30  cos ec 60, , 4.sin600.cos300+sin300.cos600, 0, 0, 6. sec 30  cos0 ec30, , cos 45, 0, 0, 8. sin 30 0 tan 45 0 cos ec 600, sec 30  cos 60  cot 45, 0, , 10., , 5 cos 2 60 0  4 sec 2 30 0  tan 2 45 0, sin 2 30 0  cos 2 30 0, , 0, 0, 12. 3 sin 60 0  2 cos ec30, 0, , tan 45  2 cot 45, , 34 cos 30 0  cos 60 0, 14., 2 sin 45 0  3 tan 45 0, 2, 45 0  2 sec 2 30 0, 16. 3 cos, 2, 0, 2, 0, , cot 30  2 cos ec 30, 2 sin 30  3 cos ec 60, 2, 0, 2, 0, 2, 0,  3 sec 2 60 0, 19. 4 sin 260 0 3 tan2 300, 17. 2 tan 45, 2, 0, 4 cos 30  sec 45, 2 cos ec 30  2 cot 2 30 0, 2, 0, 2, 0, 18. 4 cos 2 60 0  3 tan 300 20. Sin600.cos300-cos600.sin300, 5 sec 60  2 tan 45, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 16 | Page

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Practice Question Paper-1, Target-45, I. Answer the following., 7X1=7, 1.Find the distance of a point (2, -3) from the origin., 2. Find the 3rd term of AP an= 2n+3., 3.Write the formula to find Volume of cone., 4.Write condition of pair of intersection of pair of linear equation., 5.Write midpoint formula of two co-ordinates., 6.Find cosecθ if sinθ= ., 7.State Thales Theorem., II. Answer the following., 5X2=10, 8.Find the sum of A P 1+5+9+ ……upto 20 terms., 9.Draw a line segment AB of length 8 cm and divide it in the ratio of 3:2, 10.Solve x+3y=6 and 2x-3y=6., 11.Find the distance between the points (-3, 5)and (3, -3)., 12.Solve using quadratic formula x2+10x+25=0., III. Answer the following., 3X5=15, 13.Prove that, “The two tangents drawn from an external point to a circle are, equal”., 14. Draw more than ogive curve for following data., CI, 0-50, 50-100, 100-150 150-200 200-250 250-300, f, 12, 18, 27, 20, 17, 6, 15. Calculate mean, and mode for the following data distribution., C-I 0-10, 10-20, 20-30 30-40, 40-50, F, 6, 8, 7, 3, 1, 16. Draw a circle of radius 3.5 cm from a point 8 cm away from the center;, construct the pair of tangents to the circle. Measure the tangents and write., 17. Find the areas of triangles whose vertices are given below(2, -1) , (3, 2), and (5, -3), IV. Answer the following., 4X2=8, 18. Solve the following pair of linear equations in two variables by graphical, method :x + y = 7 and 3x – y = 1., 19. Construct a triangle of sides 4 cm , 5 cm and 6 cm and then a triangle similar, to it whose sides are of the corresponding sides of the first triangle., V. Answer the following., 5X1=5, 20.State and Prove, “Pythagoras theorem”., Probable date to conduct Date:02/03/2022, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 17 | Page

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Practice Question Paper-2, Target-45, , Practice Question Paper-3, Target-45, , I. Answer the following., 7X1=7, 1.Find the distance of a point (3, 4) from the origin., 2. Find the 3rd term of AP an= 3n+1., 3.Write the formula to find Volume of Hemisphere., 4.Write algebraic condition of pair of linear equation for coincident lines., 5.Write section formula to find the coordinates of a point which divides the lime, segment joining points internally in the given ratio., 6.Find tan θ if cot  = ., 7.State Pythagoras s Theorem., II. Answer the following., 5X2=10, 8. Find the sum of A P1+4+7+…………upto 30 terms., 9.Solve .2x+y=3; x+3y=18., 10. Find the distance between the points (2, 4)and (5, 8)., 11.Solve using quadratic formula 3x2-5x+2=0., 12. Draw a line segment AB of length 10 cm and divide it in the ratio of 2:3, III. Answer the following., 3X5=15, 13. “The tangent at any point of a circle is perpendicular to the radius drawn at, the point of contact”., 14. Draw less than ogive curve for following data., CI, 0-100, 100-200 200-300 300-400 400-500, F, 15, 10, 17, 12, 6, 15. Calculate median and mode for the following data distribution., C-I 0-10, 10-20, 20-30 30-40, 40-50, F, 6, 8, 7, 3, 1, 16. Draw a pair of tangents to a circle of radius 4cm, which are, inclined at an angle of 1200., 17. Find the perimeter of triangle whose vertices are (5, 2), (-3, 4) and (2, -5)., IV. Answer the following., 4X2=8, 18. Solve the following pair of linear equations in two variables by graphical, method : .2x-y-2=0; x+y=6., 19. Draw a ABC with sides AB = 5cm, BC = 4 cm and ∟ABC=600 Then, , I. Answer the following., 6X1=6, 1.Find the distance of a point (3, 0) from the origin., 2. Find the 3rd term of AP an= 3n+1., 3.Write the formula to find Volume of frustum of a cone., 4.Write algebraic condition of pair of linear equation for parallel lines., 5.Write the formula to find area of a triangle when coordinates of its vertices are, given., 6. Evaluate , tan 48o x tan 42o, II. Answer the following., 7X2=14, 8. Find the sum of A P1+4+7+…………upto 30 terms., 9.Solve .2x+y=3; x+3y=18., 10. Find the midpoint of line joining the points (3, 4)and (5, 6)., 11.Solve using quadratic formula 2x2- 3x = 5., 12. Draw a line segment PQ of length 8 cm and divide it in the ratio of 2:3, 13. Find the discriminant of equation 2x2-3x-8=0 and also write nature of roots., 14. If a12=35, a18=53 find a20, III. Answer the following., 3X4=12, 12. “The tangent at any point of a circle is perpendicular to the radius drawn at, the point of contact”., 13. Draw less than ogive curve for following data., CI, 0-10, 10-20, 20-30, 30-40, 40-50, F, 5, 7, 3, 2, 3, 14. Calculate mean and median for the following data distribution., C-I 0-5, 5-10, 10-15 15-20, 20-25, F, 6, 8, 7, 3, 1, 15 Draw a circle of radius 2.5 cm and construct a chord of length 3 cm. and, Draw the tangents at the end points of the chord., IV. Answer the following., 4X2=8, 16. Solve the following pair of linear equations in two variables by graphical, method : . y =2x-2 and y =4x-4., 17. Construct a triangle ABC with sides AB= 6cm and ∟BAC=50 0 and, ∟ABC=600. Then construct a triangle whose sides are 1 of the corresponding, sides triangle ABC., V. Answer the following., 5X1=5, 18.State and Prove, Converse of “Pythagoras theorem”., , construct a triangle whose sides are of the corresponding sides of triangle, ABC., V. Answer the following., 5X1=5, 20.State and Prove, “Thale’s theorem”., Probable date to conduct Date:05/03/2022, , Probable date to conduct Date:09/03/2022, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 18 | Page

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Practice Question Paper-4, Target-45, I. Answer the following., 7X1=7, 1.s first natural number., II. Answer the following., 6X2=12, 8. Find the sum of first 12 even natural numbers., 9.Solve . 2x+y-6=0 and 6x+2y-4=0., 10. Draw a line segment of length 7cm and divide it in the ratio of 2:1, 11.Solve using quadratic formula m2-8m+10=0., 13. If in an AP is 2,5,8… then find 20th term?, 14.If 2x2+3+5=0 then find discriminant and write nature of roots, III. Answer the following., 3X4=12, 12. “The tangent at any point of a circle is perpendicular to the radius drawn at, the point of contact”., 13. Draw ogive curve for following data., CI, >0, >10, >20, >30, >40, F, 20, 15, 8, 5, 3, 14. Calculate mean and median for the following data distribution., C-I 0-5, 5-10, 10-15 15-20, 20-25, F, 6, 8, 7, 3, 1, 15 Construct a pair of tangents to a circle of radius 3 cm from a point 6cm, away from the circle ., IV. Answer the following., 4X2=8, 16. Solve the following pair of linear equations in two variables by graphical, method : x + y =10 ; x – y =2, 17. Construct a triangle of sides 4 cm , 5 cm and 6 cm and then a triangle, similar to it whose sides are of the corresponding sides of the first triangle., V. Answer the following., 5X1=5, 18. Prove that “The areas of two similar triangles are proportional to the squares, of their corresponding side”., , Practice Question Paper-5, Target-45, I.Answer the following., 7X1=7, 1.What distance of a point P(5, -3) from the X-axis., 2. Find the 10th term of AP in which an= 6n+3., 3.Write the formula to find Volume of frustum of a cone., 4. Write condition for pair of lines a1x+b1y+c1=0 and a2x+b2y+c2=0 to be coincide., 5. Write the formula to find length of arc of sector of an angle  of circle with, radius ‘r’, 6.Find tanθ if sinθ= ., 7.State S.S.S. criterion for similarity of triangles., II. Answer the following., 5X2=10, 8.Divide the line segment AB=5.5cm in the ratio 4:3 ., 9.Find the sum of A.P. 7+5+3+ ……….. upto 30 terms., 10.Solve 3x+y=7 and 2x-y=5., 11. Find the area of the triangle whose vertices are (4, 2) (-3, 5)and (3, -3)., 12.Solve using quadratic formula 2x2+5x+10=0., II. Answer the following., 3X4=12, 13.Prove that, “The two tangents drawn from an external point to a circle are equal”., 14. Draw ogive curve for following data., CI, Less, Less, Less than Less than Less than Less than, than 50 than 100 150, 200, 250, 300, F, 12, 30, 57, 77, 94, 100, 15. Calculate mean, median and mode for the following data distribution., C-I 0-20, 20-40, 40-60 60-80, 80-100, F, 8, 10, 6, 7, 4, 16. Draw a circle of radius 4 cm from a point 8 cm away from the center; construct, the pair of tangents to the circle. Measure the tangents and write., , III. Answer the following., 4X2=8, 17. Solve the following pair of linear equations in two variables by graphical, method : 2x + y = 8 and 3x – y = 7., 18. Construct a triangle ABC in which AB=4cm AC=5cm and B  60 0 and, then a triangle similar to it whose sides are of the corresponding sides of, the first triangle., , Probable date to conduct Date:12/03/202, , IV. Answer the following., 4X2=8, 19.State and Prove, “A.A. criteria for similarity of triangles”., Probable date to conduct Date:16/03/2022, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 19 | Page

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Practice Question Paper-6, Target-45, I.Answer the following., 7X1=7, 1.Write the number of solutions that the pair of linear equations a 1x+b1y+c1=0, and a1x+b1y+c1=0 have ., 2. Write the formula to find the sum of first ‘n’ even natural numbers ., 3.If A=300, then find the value of sin3A., 4.Write the coordinates of the point ‘P’ which divides the line segment joining, the points (x1, y1) and (x2, y2) in the ratio m1:m2 internally., 5.State Basic proportionality theorem., 6.If the diameter of the circle is 14cm then find the area of its quadrant., 7.Write the formula to find the T.S.A. of hemisphere., II. Answer the following., 5X2=10, 8.Divide the line segment MN=6.3cm in the ratio 5:3 ., 9.Find the sum of A.P. 10+6+2+……….+(-98)., 10.Solve 4x+3y=17 and 5x-4y=-2., 11. Find the area of triangle whose vertices are (6, 5) (3,2) and (-1, 5)., 12.Solve using quadratic formula 4x2+7x-20=0., II. Answer the following., 3X4=12, 13.Prove that, “The radius drawn at the point of contact is perpendicular to the tangent”., 14. Draw less than ogive curve for following data., CI, More, More, More, More, More, More, than 0, than 10, than 20, than 30, than 40, than 50, F, 50, 37, 32, 25, 14, 8, 15. Calculate mean, median and mode for the following data distribution., C-I 0-15, 15-30, 30-45 45-60, 60-75, F, 8, 4, 6, 9, 3, 16. Construct two tangents to a circle of radius 4 cm which are inclined at an, angle of 750., , III. Answer the following., 4X2=8, 17. Solve the following pair of linear equations in two variables by graphical, method : 3x + y = 2 and 4x – y = 5., 18. Construct a triangle ABC in which AB=4cm A  60 0 and C  70 0 and, then a triangle similar to it whose sides are of the corresponding sides of, the first triangle, , IV. Answer the following., 4X2=8, 19. Prove that “The areas of two similar triangles are proportional to squares of, their corresponding sides”., Probable date to conduct Date:19/03/2022, , Practice Question Paper-7, Target-45, I.Answer the following., 7X1=7, 1.Find the distance of a point (2, -3) from the origin., 2. Find the 3rd term of AP an= 2n+3., 3.Write the formula to find Volume of cone., 4.Write condition of pair of intersection of pair of linear equation., 5.Write midpoint formula of two co-ordinates., 6.Find cosecθ if sinθ= ., 7.State Thales Teorem., II. Answer the following., 4X2=8, 10. Find the sum of A.P. 1+5+9+ ……….. upto 20 terms., 11. Solve x+3y=6 and 2x-3y=6., 10. Find the distance between the points (-3, 5)and (3, -3)., 11.Solve using quadratic formula x2+10x+25=0., II. Answer the following., 3X4=12, 12.Prove that, “The two tangents drawn from an external point to a circle are, equal”., 13. Draw more than ogive curve for following data., CI, 0-50, 50-100, 100-150 150-200 200-250 250-300, f, 12, 18, 27, 20, 17, 6, 14. Calculate mean, median and mode for the following data distribution., C-I 0-10, 10-20, 20-30 30-40, 40-50, F, 6, 8, 7, 3, 1, 15. Draw a circle of radius 3.5 cm from a point 8 cm away from the center;, construct the pair of tangents to the circle. Measure the tangents and write., III. Answer the following., 4X2=8, 16. Solve the following pair of linear equations in two variables by graphical, method :x + y = 7 and 3x – y = 1., 17. Construct a triangle of sides 4 cm , 5 cm and 6 cm and then a triangle similar, to it whose sides are of the corresponding sides of the first triangle., IV. Answer the following., 4X2=8, 18.State and Prove, “Pythagoras theorem”., , Probable date to conduct Date:22/03/2022, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 20 | Page

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Practice Question Paper-8, Target-45, I.Answer the following., 7X1=7, 1.Find the distance of a point (2, -3) from the origin., 2. Find the 3rd term of AP an= 2n+3., 3.Write the formula to find Volume of cone., 4. Write condition for pair of lines a1x+b1y+c1=0 and a2x+b2y+c2=0 to be, intesect., 5.Write midpoint formula of two co-ordinates., 6.Find cosecθ if sinθ= ., 7.State Thales Teorem., II. Answer the following., 5X2=10, 8.Divide the line segment AB=8cm in the ratio 3:2 ., 9.Find the sum of A.P. 1+5+9+ ……….. upto 20 terms., 10.Solve x+3y=6 and 2x-3y=6., 11. Find the distance between the points (-3, 5)and (3, -3)., 12.Solve using quadratic formula x2+10x+25=0., II. Answer the following., 3X4=12, 13.Prove that, “The two tangents drawn from an external point to a circle are, equal”., 14. Draw more than ogive curve for following data., CI, 0-50, 50-100, 100-150 150-200 200-250 250-300, F, 12, 18, 27, 20, 17, 6, 15. Calculate mean, median and mode for the following data distribution., C-I 0-10, 10-20, 20-30 30-40, 40-50, F, 6, 8, 7, 3, 1, 16. Draw a circle of radius 3.5 cm from a point 8 cm away from the center;, construct the pair of tangents to the circle. Measure the tangents and write., III. Answer the following., 4X2=8, 17. Solve the following pair of linear equations in two variables by graphical, method :x + y = 7 and 3x – y = 1., 18. Construct a triangle of sides 4 cm , 5 cm and 6 cm and then a triangle similar, to it whose sides are of the corresponding sides of the first triangle., IV. Answer the following., 4X2=8, 19.State and Prove, “Pythagoras theorem”., , Practice Question Paper-9, Target-45, I.Answer the following., 7X1=7, 1.Find the distance of a point (3, 2) from the origin., 2. Find the 5th term of AP in which an= 5n-3., 3.Write the formula to find the area of sector of an angle  of circle with, radius ‘r’., 4.Write condition for pair of lines a1x+b1y+c1=0 and a2x+b2y+c2=0 to be, parallel., 5.State A.S.A. criteria for similarity of triangles., 6.Find cosθ if secθ= ., 7.Write the formula to find the T.S.A. of cylinder., II. Answer the following., 5X2=10, 8.Divide the line segment PQ=7cm in the ratio 1:2 ., 9.Find the sum of A.P. 1+4+7+……….+100., 10.Solve 3x+2y=6 and 5x-3y=8., 11. Find the midpoint of the points (-3, 5)and (3, -3)., 12.Solve using quadratic formula x2+6x-30=0., II. Answer the following., 3X4=12, 13.Prove that, “The radius drawn at the point of contact is perpendicular to the, tangent”., 14. Draw less than ogive curve for following data., CI, 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, F, 5, 3, 4, 6, 3, 4, 15. Calculate mean, median and mode for the following data distribution., C-I 0-5, 5-10, 10-15 15-20, 20-25, F, 6, 4, 7, 2, 1, 16. Construct two tangents to a circle of radius 4 cm which are inclined at an, angle of 650., III. Answer the following., 4X2=8, 17. Solve the following pair of linear equations in two variables by graphical, method : 2x + y = 5 and 3x – y = 5., 18. Construct a triangle of sides 3cm , 4 cm and 5 cm and then a triangle similar, to it whose sides are of the corresponding sides of the first triangle., IV. Answer the following., 4X2=8, 19.State and Prove, “Thales theorem”., , Probable date to conduct Date:25/03/2022, , Probable date to conduct Date:02/04/2022, , SSLC -2021-22 PASSING PACKGE PREPARED BY KREIS, BANGLORE, , 21 | Page